This musical centered around the life of Annie Oakley and starred Betty Hutton in the title role (although Judy Garland was famously cast first). 

Opening title shots feature shots of a steam engine pulling Buffalo Bill's Wild West show across the country. However, upon closer inspection it becomes obvious that this is a model. 

Buffalo Bill and gang erupt into song to announce their arrival in town. Virginia & Truckee #11 "Reno" leads the train followed by Combine Coach #20 and Coach #19. These were all owned by MGM at the time, and this was filmed on the "Small Town Square" portion of MGM's Lot 2 (now demolished). 

Today, the Reno is on display in Virginia City awaiting restoration and Coach #20 is at NSRM awaiting restoration. Coach #19 was burned in a fire at Old Tucson. 

For traveling montage shots, they use a mixture of model shots, actors looking out the actual passenger coach windows, and stock footage of Sierra RR #18 borrowed from Dodge City. A fair amount of process shots were also done, likely with replica cars on stage at MGM. 

At some point, the train cars were moved to MGM's Lot 3 for the "circus tent" scenes. This giant set was left after filming and utilized for other productions on the lot. This lot was also eventually sold off and developed. 

The ocean liner was also a standing set at MGM's Lot 3.